Preheat the oven to 500 degrees F.,For the parsley pesto: Add the Parmigiano-Reggiano, pine nuts, basil, garlic, parsley and some salt and pepper to a food processor.,With the motor running, slowly add about 1/2 cup olive oil and process until smooth.,Pulse a few times to incorporate, adding more oil if the mixture is too thick.,Taste and adjust the seasoning if needed.,For the mushrooms: Heat the canola oil in a large saute pan over medium-high heat until almost smoking.,Add the mushrooms, garlic and shallots and saute until brown, about 5 minutes.,Season with salt and pepper.,Remove to a plate and reserve.,Preheat a grill pan over medium-high heat.,______,Dust a work surface with flour and roll each piece of dough into a rectangle (or whatever shape you like).,Brush the tops of each piece with oil, sprinkle with salt and pepper and toss on the grill, oil-side down.,Cook until the bottoms are an even golden brown, about 3 minutes.,(The tops will also start bubbling up with air pockets.),Flip over and grill until golden brown on the other side and just firm, about a minute or so.,Remove to a baking sheet.,Top the pizzas with the fontina, mushrooms, Parmigiano-Reggiano, dollops of goat cheese, crushed red pepper flakes and salt and pepper.,Bake in the oven until the cheese is melted, 3 to 4 minutes.,Top with the parsley pesto and garnish with a few more torn basil leaves.